The representation of various objects by data compression is a problem with which the art has been increasingly occupied in recent times. The problem is encountered in many cases, e.g. when a picture, or a succession of pictures, for example constituting a television broadcast, has to be registered in a magnetic memory, such as a video tape, or is to be transmitted over a distance by electromagnetic waves or by cable. On the one hand, it is of considerable economic importance to increase as much as possible the amount of optical and acoustic information that can be registered on a given memory, whereby to reduce the size and cost of magnetic tapes or other information storage means. On the other hand, the available wave bands are increasingly crowded, and so are the cables, and it is increasingly necessary to compress the transmitted data, so that as great a number of them as possible may be transmitted over a given frequency or by a given cable. Data compression problems, therefore, are increasingly acute, both in data storage and in data transmission.
In particular, the art has dealt with the problem of compressing the data which represent an object, e.g. a picture. A process for the production of images of objects is disclosed in EPA 0 465 852 A2, which process comprises the steps of: (1) approximating the object by a model comprising at least one differentiable component; (2) establishing the maximum allowable error and the degree of the polynomials by which the differentiable components of the model are to be approximated; (3) constructing a grid of a suitable pitch; (4) computing the coefficients of the Taylor polynomials of the aforesaid differentiable components at selected points of said grid.
However, none of the method and apparatus of the prior art are wholly satisfactory. Either the degree of compression is too small, or the picture cannot be faithfully reconstructed--viz. "decompressed"--from the compressed data, or both. There is another important requirement, not satisfied by known compression methods: application of image processing operations on compressed data, and natural extendibility of the compression scheme to video sequences compression.
In describing this invention, two-dimensional pictures, in particular color pictures, such as those created on a television screen, are considered, but three- or more than three-dimensional objects could be represented by the apparatus and method provided by the invention, e.g. by defining them by means of views or cross-sections in different planes.
The efficiency of a compression method depends on the one hand on the degree of compression, which should be as high as possible, but on the other on the faithfulness with which the picture reconstructed from the compressed data reproduces the original one. Perfect reproduction is obtained when the two pictures are visually undistinguishable. Two pictures are considered to be "visually undistinguishable", as defined by the MPEG (Motion Picture Expert Group of the International Standard Organization), when any ordinary viewer cannot distinguish between them when viewing them from a distance equal to six times the picture height. Different requirements for visual undistinguishability may be defined for different applications, such as: high end computer imaging, PC computer imaging, PC or video games, multimedia, pre-press applications, fax, colour video conferencing, videophone, archiving, medical imaging, aerial picture analysis, etc. However, the invention does not always require that the picture representation and the original be visually undistinguishable, though this is generally preferred: the degree of similarity may depend on the particular application and on the degree of faithfulness that is required of the representation in each case.